A gambler offers to let you play the following game: he will roll two (fair) dice. If the sum of the two dice is 7, you will lose $8. If the sum of the two dice is 2, you will lose $7. For any other roll, you will win $4. What is the expected value of this gamble?

Answer 1

Prob(7) = 1/6
Prob(2) = 1/36
Prob(neither a 7 nor a 2) = 1 - 1/6 - 1/36 = 29/36

expected value = -(1/6)(8.00) - (1/36)(7.00) + (29/36)(4.00)
= .....